Journal of Computational Neuroscience

, Volume 19, Issue 2, pp 223–238 | Cite as

Local Diameter Fully Constrains Dendritic Size in Basal but not Apical Trees of CA1 Pyramidal Neurons

  • Duncan E. Donohue
  • Giorgio A. Ascoli


Computational modeling of dendritic morphology is a powerful tool for quantitatively describing complex geometrical relationships, uncovering principles of dendritic development, and synthesizing virtual neurons to systematically investigate cellular biophysics and network dynamics. A feature common to many morphological models is a dependence of the branching probability on local diameter. Previous models of this type have been able to recreate a wide variety of dendritic morphologies. However, these diameter-dependent models have so far failed to properly constrain branching when applied to hippocampal CA1 pyramidal cells, leading to explosive growth. Here we present a simple modification of this basic approach, in which all parameter sampling, not just bifurcation probability, depends on branch diameter. This added constraint prevents explosive growth in both apical and basal trees of simulated CA1 neurons, yielding arborizations with average numbers and patterns of bifurcations extremely close to those observed in real cells. However, simulated apical trees are much more varied in size than the corresponding real dendrites. We show that, in this model, the excessive variability of simulated trees is a direct consequence of the natural variability of diameter changes at and between bifurcations observed in apical, but not basal, dendrites. Conversely, some aspects of branch distribution were better matched by virtual apical trees than by virtual basal trees. Dendritic morphometrics related to spatial position, such as path distance from the soma or branch order, may be necessary to fully constrain CA1 apical tree size and basal branching pattern.


computational models dendritic structure morphology pyramidal cells three-dimensional reconstructions 


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  1. Ascoli GA (2002) Computing the brain and the computing brain. In: G Ascoli ed. Computational Neuroanatomy: Principles and Methods. Humana Press, Totowa, NJ, pp. 3–23.Google Scholar
  2. Ascoli GA, Krichmar JL (2000) L-Neuron: A modeling tool for the efficient generation and parsimonious description of dendritic morphology. Neurocomputing 32–33: 1003–1011.Google Scholar
  3. Ascoli GA, Krichmar JL, Nasuto SJ, Senft SL (2001a) Generation, description and storage of dendritic morphology data. Philos. Trans. R. Soc. Lond. B. Biol. Sci. 356(1412): 1131– 1145.CrossRefGoogle Scholar
  4. Ascoli GA, Krichmar JL, Scorcioni R, Nasuto SJ, Senft SL (2001b) Computer generation and quantitative morphometric analysis of virtual neurons. Anat. Embryol. (Berl.) 204(4): 283–301.CrossRefGoogle Scholar
  5. Buckmaster PS, Alonso A, Canfield DR, Amaral DG (2004) Dendritic morphology, local circuitry, and intrinsic electrophysiology of principal neurons in the entorhinal cortex of macaque monkeys. J. Comp. Neurol. 470(3): 317–329.Google Scholar
  6. Berezovska O, McLean P, Knowles R, Frosh M, Lu FM, Lux SE, Hyman BT (1999) Notch1 inhibits neurite outgrowth in postmitotic primary neurons. Neuroscience 93(2): 433–439.CrossRefPubMedGoogle Scholar
  7. Buettner HM (1995) Computer simulation of nerve growth cone filopodial dynamics for visualization and analysis. Cell. Motil. Cytoskeleton 32(3): 187–204.CrossRefPubMedGoogle Scholar
  8. Buettner HM, Pittman RN, Ivins JK (1994) A model of neurite extension across regions of nonpermissive substrate: Simulations based on experimental measurement of growth cone motility and filopodial dynamics. Dev. Biol. 163(2): 407–422.CrossRefPubMedGoogle Scholar
  9. Burke RE, Marks WB, Ulfhake B (1992) A parsimonious description of motoneuron dendritic morphology using computer simulation. J. Neurosci. 12(6): 2403–2416.PubMedGoogle Scholar
  10. Cannon RC, Turner DA, Pyapali GK, Wheal HV (1998) An on-line archive of reconstructed hippocampal neurons. J. Neurosci. Methods 84(1/2): 49–54.CrossRefPubMedGoogle Scholar
  11. Carriquiry AL, Ireland WP, Kliemann W, Uemura E (1991) Statistical evaluation of dendritic growth models. Bull. Math. Biol. 53(4): 579–589.CrossRefPubMedGoogle Scholar
  12. Costa Lda F, Manoel ET (2003) A percolation approach to neural morphometry and connectivity. Neuroinformatics 1(1): 65–80.CrossRefPubMedGoogle Scholar
  13. Dailey ME, Smith SJ (1996) The dynamics of dendritic structure in developing hippocampal slices. J. Neurosci. 16(9): 2983–2994.PubMedGoogle Scholar
  14. Donohue DE, Scorcioni R, Ascoli GA (2002) Generation and description of neuronal morphology using L-Neuron: A case study. In: G Ascoli, ed. Computational Neuroanatomy: Principles and Methods. Humana Press, Totowa, NJ. pp. 49–70.Google Scholar
  15. Donohue DE, Scorcioni R, Ascoli GA (2003) Diameter dependent morphological models of hippocampal CA1 pyramidal cell dendrites. Poster 144.13 at The Society for Neuroscience 2003 Annual Meeting, New Orleans, LA.Google Scholar
  16. Donohue DE, Ascoli GA (2005) Models of neuronal outgrowth. In: SH Koslow and S Subramaniam, ed. Databasing the Brain: From Data to Knowledge. Wiley Press, Hoboken, NJ. pp. 303–323.Google Scholar
  17. Fukushima N, Weiner JA, Kaushal D, Contos JJ, Rehen SK, Kingsbury MA, Kim KY, Chun J (2002) Lysophosphatidic acid influences the morphology and motility of young, postmitotic cortical neurons. Mol. Cell. Neurosci. 20(2): 271–282.CrossRefPubMedGoogle Scholar
  18. Gao FB, Brenman JE, Jan LY, Jan YN (1999) Genes regulating dendritic outgrowth, branching, and routing in Drosophila. Genes. Dev. 13(19): 2549–2561.CrossRefPubMedGoogle Scholar
  19. Goodhill GJ, Urbach JS (1999) Theoretical analysis of gradient detection by growth cones. J. Neurobiol. 41(2): 230–241.CrossRefPubMedGoogle Scholar
  20. Häusser M, Mel B (2003) Dendrites: Bug or feature? Curr. Opin. Neurobiol. 13(3): 372–383.CrossRefGoogle Scholar
  21. Hely TA, Graham B, van Ooyen A (2001) A computational model of dendrite elongation and branching based on MAP2 phosphorylation. J. Theor. Biol. 210(3): 375–384.CrossRefPubMedGoogle Scholar
  22. Hillman DE (1979) Neuronal shape parameters and substructures as a basis of neuronal form. In: F Schmitt, ed. The Neurosciences, Fourth Study Program. MIT Press, Cambridge, MA. pp. 477–498.Google Scholar
  23. Ireland W, Heidel J, Uemura E (1985) A mathematical model for the growth of dendritic trees. Neurosci. Lett. 54(2/3): 243–249.PubMedGoogle Scholar
  24. Ishizuka N, Cowan WM, Amaral DG (1995) A quantitative analysis of the dendritic organization of pyramidal cells in the rat hippocampus. J. Comp. Neurol. 362(1): 17–45.CrossRefPubMedGoogle Scholar
  25. Kliemann W (1987) A stochastic dynamical model for the characterization of the geometrical structure of dendritic processes. Bull. Math. Biol. 49(2): 135–152.CrossRefPubMedGoogle Scholar
  26. Koch C, Segev I (2000) The role of single neurons in information processing. Nat. Neurosci. 3(Suppl): 1171–1177.CrossRefPubMedGoogle Scholar
  27. Kryl D, Yacoubian T, Haapasalo A, Castren E, Lo D, Barker PA (1999) Subcellular localization of full-length and truncated Trk receptor isoforms in polarized neurons and epithelial cells. J. Neurosci. 19(14): 5823–5833.PubMedGoogle Scholar
  28. Luo L (2002) Actin cytoskeleton regulation in neuronal morphogenesis and structural plasticity. Annu. Rev. Cell. Dev. Biol. 18: 601–635.CrossRefPubMedGoogle Scholar
  29. Mainen ZF, Carnevale NT, Zador AM, Claiborne BJ, Brown TH (1996) Electrotonic architecture of hippocampal CA1 pyramidal neurons based on three-dimensional reconstructions. J. Neurophysiol. 76(3): 1904–1923.PubMedGoogle Scholar
  30. Mainen ZF, Sejnowski TJ (1996) Influence of dendritic structure on firing pattern in model neocortical neurons. Nature 382(6589): 363–366.CrossRefPubMedGoogle Scholar
  31. Megias M, Emri Z, Freund TF, Gulyas AI (2001) Total number and distribution of inhibitory and excitatory synapses on hippocampal CA1 pyramidal cells. Neuroscience 102(3): 527–540.CrossRefPubMedGoogle Scholar
  32. Notomi T, Shigemoto R (2004) Immunohistochemical localization of Ih channel subunits, HCN1-4, in the rat brain. J. Comp. Neurol. 471(3): 241–276.CrossRefPubMedGoogle Scholar
  33. Pyapali GK, Sik A, Penttonen M, Buzsaki G, Turner DA (1998) Dendritic properties of hippocampal CA1 pyramidal neurons in the rat: Intracellular staining in vivo and in vitro. J. Comp. Neurol. 391(3): 335–352.CrossRefPubMedGoogle Scholar
  34. Rall W, Burke RE, Holmes WR, Jack JJB, Redman SJ, Segev I (1992) Matching dendritic neuron models to experimental data. Physiol. Revs. 72: S159–S186.Google Scholar
  35. Redmond L, Ghosh A (2002) The role of Notch and Rho GTPase signaling in the control of dendritic development. Curr. Opin. Neurobiol. 11(1): 111–117.CrossRefGoogle Scholar
  36. Samsonovich AV, Ascoli GA (2003) Statistical morphological analysis of hippocampal principal neurons indicates cell-specific repulsion of dendrites from their own cell. J. Neurosci. Res. 71(2): 173–187.CrossRefPubMedGoogle Scholar
  37. Samsonovich AV, Ascoli GA (2005) Statistical determinants of dendritic morphology in hippocampal pyramidal neurons: A hidden Markov model. Hippocampus 15(2): 166–183.CrossRefPubMedGoogle Scholar
  38. Schaefer AT, Larkum ME, Sakmann B, Roth A (2003) Coincidence detection in pyramidal neurons is tuned by their dendritic branching pattern. J. Neurophysiol 89(6): 3143–3154.PubMedGoogle Scholar
  39. Scorcioni R, Ascoli, GA (2001) Algorithmic extraction of morphological statistics form electronic archives of neuroanatomy. Lect. Notes Comp. Sci. 2084: 30–37.Google Scholar
  40. Scorcioni R, Lazarewicz MT, Ascoli GA (2004) Quantitative morphometry of hippocampal pyramidal cells: Differences between anatomical classes and reconstructing laboratories. J. Comp. Neurol. 473(2): 177–193.CrossRefPubMedGoogle Scholar
  41. Stepanyants A, Tamas G, Chklovskii DB (2004) Class-specific features of neuronal wiring. Neuron 43(2): 251–259.CrossRefPubMedGoogle Scholar
  42. Szilagyi T, De Schutter E (2004) Effects of variability in anatomical reconstruction techniques on models of synaptic integration by dendrites: A comparison of three Internet archives. Eur. J. Neurosci. 19(5): 1257–1266.CrossRefPubMedGoogle Scholar
  43. Tang BL (2003) Inhibitors of neuronal regeneration: Mediators and signaling mechanisms. Neurochem. Int. 42(3): 189–203.CrossRefPubMedGoogle Scholar
  44. Uemura E, Carriquiry A, Kliemann W, Goodwin J (1995) Mathematical modeling of dendritic growth in vitro. Brain. Res. 671(2): 187–194.CrossRefPubMedGoogle Scholar
  45. van Pelt J, Dityatev AE, Uylings HB (1997) Natural variability in the number of dendritic segments: Model-based inferences about branching during neurite outgrowth. J. Comp. Neurol. 387(3): 325–340.CrossRefPubMedGoogle Scholar
  46. van Veen MP, van Pelt J (1994a) Dynamic mechanisms of neuronal outgrowth. Prog. Brain. Res. 102: 95–108.Google Scholar
  47. van Veen MP, van Pelt J (1994b) Neuritic growth rate described by modeling microtubule dynamics. Bull. Math. Biol. 56(2): 249–273.CrossRefGoogle Scholar
  48. Vetter P, Roth A, Hausser M (2001) Propagation of action potentials in dendrites depends on dendritic morphology. J. Neurophysiol. 85(2): 926–937.PubMedGoogle Scholar
  49. Whitford KL, Dijkhuizen P, Polleux F, Ghosh A (2002) Molecular control of cortical dendrite development. Annu. Rev. Neurosci. 25: 127–149.CrossRefPubMedGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Krasnow Institute for Advanced StudyGeorge Mason UniversityFairfaxUSA
  2. 2.Department of PsychologyGeorge Mason UniversityFairfaxUSA
  3. 3.Krasnow Institute for Advanced StudyGeorge Mason UniversityFairfaxUSA

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